In this paper we study and analyze the in uence of caching stategies on the performance of WWW proxies. We propose a new strategy called class-based LRU that works recency-based as well as size-based, with the ultimate aim to obtain a well-balanced mixture between large and small documents in the cache, and hence, good performance for both small and large object requests. We show that for class-based LRU good results are obtained for both the hit rate and the byte hit rate, if the size of the classes and the corresponding document size ranges are well choosen. The latter is achieved by using a Bayesian decision rule and a characterisation of the requested object-size distribution using the EM-algorithm. Furthermore, the overhead to implement class-based LRU is comparable to that of LRU and does not depend on the number of cached objects.